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The Saudi transit visa you referred to is a type of visa that allows you go out and discover whatever city you are transiting, it is not meant for air-side transit, which is allowed for any layover less than 12 hrs without any visa.
However, if you hold a passport from one of these countries, you are eligible for a visa on arrival. Also, if you hold a VALID US, UK or a Schengen visa that has been used at least once (with a stamp as a proof) then you are eligible for the visa on arrival regardless of your nationality.